Model of 5R Spatial Linkage in the Geometry of Tori

Abstract

The present study covers the problem of a kinematic analysis of a spatial 5R single DOF linkage. This mechanism was constructed by combining two 4R universal mechanisms presented in tori geometry . The problem can be presented as the effect of an intersection of two tori in such a manner that the circles that form these tori do not coincide (Bil, 2010;2011;. As a result of this, a 5R model was obtained of a five-bar mechanism. It was demonstrated that there are 16 cases of the intersection of two universal tori with constant linear dimensions and that they differ with the angles of the mutual positions of rotation axes. A particular case of the five-bar mechanism presented herein is the well-known Goldberg mechanism (Goldberg, 1943), which was initially formed out of a particular case combination of two Bennett mechanisms (Bennett, 1903;Baker, 1979).

Modelling and Motion Analysis of Five-Bar 5R Mechanism

“…The primary element in the process of designing or an analysis of mechanical systems that use computer aided processes is the creation of a virtual model of a spatial multi-membered mechanism including its appropriate elements. In the first stage of the creation of this model, one of the following concepts can be selected:  3D parametric edge modelling of the arms of the mechanism (Bil and Budniak, 2012), and further making an assembly in accordance with the data contained in the mathematical model (Bil, 2012a;2012b;Bil and Budniak, 2014);  modelling of a spatial measurement chain in CAD software, and further modelling of the arms and the assembly of the mechanism with the use of constructive geometry (constructional planes, axes and points, as well as local coordinate systems: related to the elements of the spatial measurement chain).…”

“…In the present study, an analysis was conducted of a spatial five-membered lever mechanism 5R that was constructed based on the mathematical model presented in the article (Bil and Budniak, 2014). Such a mechanism with five rotational pairs ( Fig.1) will be formed when in the common point S=S 2 =R 4 there will exist a kinematic pair with a common axis.…”

“…Owing to the use of the SolidWorks Motion software (Chan, 2011), it was possible to find the positions of the characteristic points of the members. The positions of these points are sought on their trajectories that are the result of those constraints (of lengths and angles) that are imposed by the individual members and kinematic pairs (Bil and Budniak, 2014).…”